On the Complexity of Finding Shortest Variable Disjunction Branch-and-Bound Proofs

We investigate the complexity of finding small branch-and-bound trees using variable disjunctions. We first show that it is not possible to approximate the size of a smallest branch-and-bound tree within a factor of 2^(1/5) in time 2^(\delta n) with \delta < 1/5, unless the strong exponential time hypothesis fails. Similarly, for any \varepsilon > 0, … Read more